Right after the formulation of the AdS/CFT conjecture, some tree-level Witten diagrams were computed by conventional methods [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, but more efficient and illuminating techniques were developed only recently starting with the introduction of the Mellin representation of correlation functions for conformal field theories constructed by Mack [7]} and further developed in [8]}, [9]}. Even more recently, a new formalism called geodesic-Witten diagrams, that emulate the conformal block expansion of correlation functions from the gravity perspective, have been developed in [10]} and extended to the inclusion of spinning particles in [11]}, [12]}, [13]}, [14]}, [15]}. However, despite those very interesting technical developments, the computation of loop Witten diagrams have proven to be very challenging and keeps being very unexplored. With the exception of few previous considerations [8]}, [17]}, [18]}, [19]} and some recent progress in, not even the most basic scalar loop integrals have been computed yet.
